Problem 3.306

A plane spiral with a great number $N$ of turns wound tightly to one another is located in a uniform magnetic field perpendicular to the spiral's plane. The outside radius of the spiral's turns is equal to $a$. The magnetic induction varies with time as $B=B_{0} \sin \omega t,$ where $B_{0}$ and $\omega$ are constants. Find the amplitude of emf induced in the spiral.